4056
H. KWART,S. F. SARNER,AND J. H. OLSON
Homogeneous Gas-Phase Thermolysis Kinetics. An Improved Flow Technique for Direct Study of Rate Processes in the Gas Phase
by Harold Kwart, Stanley F. Sarner, and Jon H. Olson Departments o j Chemistry and Chemical Engineering, University o j Delaware, Newark, Delaware (Received February 18,1969)
19711
The operational parameters of an improved flow method for direct determination of the kinetics of gas-phase thermolysis reactions have been evaluated. A scheme has been devised for rapidly estimating the rates of first-order decompositions in a single series of simple measurementsat an established reactor temperature. The activation parameters for decomposition of ethyl acetate and dicyclopentadiene have been determined in this fashion and compared with the corresponding values reported by earlier authors applying a variety of kinetic techniques. The use of a gold-surfacedreactor and a highly diluted reaction medium has simplified (or eliminated) the problem of residual wall reaction.
Introduction The application of flow methods to the study of the kinetics of homogeneous gas-phase reactions is highly advantageous since a time-invariant concentration gradient is The reactor described herein is a flow reactor in which many difficulties present in other designs have been eliminated. On entering the system the reactant is immediately diluted with a large volume of helium, thus precluding intermolecular reactions, simplifying the analysis to considerations of unimolecular mechanisms, and rendering the effects of volume changes during reaction (due to changes in the number of moles) negligible. The design results in laminar flow with a low degree of axial diffusion in the reactor, thereby simplifying the kinetics to the case of the static reactor model under normal operating conditions. The reactor system is equipped with a preliminary gas chromatograph, so that samples may be purified and directly transferred to the reactor, and a second gas chromatograph providing for automatic analysis of the reaction products. The helium flows in the three sections of the system (GC1, reactor, and GC2) are separate, allowing each gas chromatograph to be operated under optimum conditions for analysis while providing for maximum variability of reactor residence time. The elements of the design of this reactor system and its application to kinetic measurements are discussed below. Data obtained for the thermolysis of ethyl acetate and dicyclopentadiene are also presented and compared to those in the literature obtained by other methods. Apparatus and Operation The reactor system is similar to the model described by Levy.5 The basic block diagram is shown in Figure 1, and the flow diagram of the reactor module is shown The Journal of Physical Chemistry
in Figure 2. In a typical experiment a sample is injected into GC1 and a normal chromatogram is obtained using a nondestructive thermal conductivity detector. The 4-port 2-position selector valve (A) in the position shown simply vents the output of GC1. Upon rotation of this valve 90” clockwise, the sample plus helium from GC1 is directed into the reactor module. The valve is then returned to its original position, and the regulated helium flow of the reactor module assumes control of the sample. Alternatively, a sample can be directly injected into a port in line with the reactor helium flow, and this will be directed into. the reactor without rotating the valve. The sample is moved through the delay coil (D) into port 1 of the 4-port 2-position bypass valve (B), out of port 2 into the reactor coil, and then back through the bypass valve (ports 4 and 3) to the indicator thermal conductivity cell. If the bypass valve is rotated go”, the reactor coil is bypassed for system checking or calibration of GC2. From the indicator cell, the sample is directed into port 4 of the transfer valve (C), out of port 5 , and through the transfer coil (E) back through ports 2 and 3 of the transfer valve to the other side of the indicating cell, and then vented. This latter path through the indicating cell can be eliminated if desired since the path volume after the first indication is known and the transfer time can be determined from the volume flow rate. With two indications, the determination of the time at which the
(1) W. D. Walters in “Technique of Organic Chemistry,” Vol. 8, Interscience Publishers, New York, N . Y., 1953,p 231. (2) A. Maccoll in “Technique of Organic Chemistry,” Vol. 8, Interscience Publishers, New York, N . Y., 1953,p 427. (3) H.B. Young and L. P. Hammet, J. Amer. Chem. Soc., 7 2 , 280 (1950); J. Suldick and L. P. Hammet, ibid., 72, 283 (1950);L. B. Rand and L. P. Hammet, ibid., 72, 287 (1950). (4) J. DeGraaf and H. Kwart, J . Phys. Chem., 67, 1458 (1963); J. DeGraaf, Thesis, Leiden, Netherlands, 1961. (5) E. J. Levy and D . G. Paul, J . Gas Chromatogr., 5, 136 (1967).
4057
HOMOGENEOUS GAS-PHASETHERMOLYSIS KINETICS A.TRANSFER TIME SET-UP
tl"'
t INJECTOR
Figure 1.
B. PYROLYZATE TRANSFER V2 VENT ,(FLOW
I I
METER)
I.! To GC No'
-*.(LVENT I !
I IIIA---J &3J
I
w-4 Figure 3. . SAMPLE )M EXIT NO. I
A L L EXTERNAL LINES 1/8" SS AND THERMOSTATED AT 25O-30O0C.
Hedl FLOW 'ONTROLLER
CONTROLLER
Figure 2.
sample (now reacted) is in the center of the transfer coil is simplified as shown in Figure 3. For succeeding runs under the same conditions, the same procedure is followed until the predetermined time (from Figure 3) at which the reaction products are in the center of the transfer coil. At this time, the transfer valve (C) is rotated 60" so that the GC2 helium flow back flushes the sample in the transfer coil into GC2 for analysis. At the same time, the reactor flow is directed to the indicating cell, and the lack of any further display (Figure 3b) shows that no portion of the sample has failed to be transmitted to the GC2. The operation of chromatographs GC1 and GC2 is no different than normal, except that the output from port 6 of the transfer valve is fitted to the injection port of GC2 for automatic transfer rather than requiring sample collection and subsequent injection. The inclusion of the transfer coil and valve allows each of the three flows in the system (GC1, reactor, and GC2) to be entirely independent, so that each chromatographic flow can be optimized for the required separations and so that the reactor flow can be varied to obtain a variety of reaction conditions. I n one of the systems used in this investigation, GC1 is a programmed temperature gas chromatograph (Hewlett-Packard Model 700 series with Model 240 temperature programmer), equipped with a nondestructive dual thermal conductivity detector, and GC2 is a programmed temperature gas chromatograph (Hewlett-Packard Model 5750) with a dual flame ionization detector for increased sensitivity. I n two other systems, no GC1 is employed, and GC2 uses a thermal conductivity detector. The reactors consist of gold coils helically wound on
stainless steel cores 1.75 in. in diameter and extending past the ends of the helices so that all gradients are beyond the reactor coils. I n two systems, the coils have inside diameters of 0.0937 in. and lengths of 36 and 32.5 in., resulting in volumes of 4.07 and 3.67 ml, respectively. The third reactor coil in use has a 0.221 in. i.d. and is 33.25 in. long, giving a volume of 20.90 ml. They are heated by means of cartridge heaters and regulated by temperature controllers (Hewlett-Packward Model 220 or equivalent) and can accurately maintain desired reaction temperatures up to 675". The delay and transfer coils are "16411. 0.d. stainless steel, with the latter being 25 ft in length; all internal connecting lines are 0.125-in. i.d. stainless steel tubing; the valves have glass-filled Teflon seats; the external connections and the reactor module are thermostated at a suitable temperature between the condensation and reaction temperatures. The delay coil must be sufficiently long to contain a complete peak so that the selector valve (A) may be turned to allow control of the flow by the reactor flow prior to entry to the reactor. A modification has been made in one of the systems presently in use to split the reactor flow after the first indication to direct half the flow through another valve for a detailed thermal conductivity detected analysis on a second column in addition to the main analysis on GC2. This section provides added information on smaller molecules such as CH4, CO, COz, HzO, NH3, HC1, HBr, CZH4, Ci", and C3H6, for which results under CG2 conditions optimized for larger molecule analyses may not be definitive. This reaction was not required in this work except to determine that no "small molecule" other than CzH4 was present and will not be described here. Recently, Levy and Paul6 described a model of this reactor system from which the present equipment is an outgrowth. Their results, in experiments using the Volume 73, Number I2 December 1969
4058 reactor in free-radical pyrolytic cracking of hydrocarbons and long-chain molecules with functional group terminations, showed that the thermolytic dissociation patterns were independent of sample size, reproducible under standardized conditions, correlatable with the molecular structure of the reactant, and agreed with the results predicted by the modified Rice free-radical mechanism theory.6 Thus, it was anticipated that this experimental approach would be applicable to homogeneous gas-phase kinetic reactions.
Data Acquisition Basically, only three parameters are required to characterize the reaction kinetics, i.e., the contact time, the reaction temperature, and the extent of reaction. The first is easily obtained from the known reactor volume and the volume flow rate. This latter is measured under ambient conditions using a soap film meter and vents provided in the apparatus for such measurement. The reactor temperature is measured via a chromelalumel thermocouple and a potentiometer. These are combined to give the residence time as
where V is the reactor volume, F is the volume flow rate measured by the soap film meter, T is temperature, P is pressure, and the subscripts m and r refer to the soap film meter and reactor measurements, respectively. For this work, the ratio Pr/P, was taken as unity, since both the reactor and the soap film meter were at ambient pressure. The extent of the reaction is determined either by an internal standard technique or by reference to the total integral. I n the first case, accurate mixtures of the reactant and an unreactive standard are made and diluted with an unreactive solvent until the chromatographic response to variation in concentration ratios of reactant to standard is linear over the desired range. Comparison of the reactant to standard ratio between bypass and thermolysis conditions on the same sample then gives the ratio of reactant concentrations before and after thermolysis under the experimental conditions. I n the second method, where pure substrate only is transferred from GC1, the total product integral can be taken equal to the unreacted substrate, and the same ratio can be determined. Analysis of the operating conditions of the reactors as given below has established that the systems are essentially static reactors. Thus, at any temperature, the specific reaction rate constant, k, is given by
where Co and C are the initial and final substrate concentrations, respectively, and r is the residence time. It should be noted that C/Co will be determined chroThe Journal o j Physical Chemistry
H. KWART,S. F. SARNER, AND J. H. OLSON matographically and is subject to errors of the order of 301,. Inspection of the relationship of C/C0 us. -In (C/Co) will show that at small values of C/Co the determination of the rate constant is subject to the largest errors from this source. Similarly, since the Arrhenius relationship will ultimately be used, and In k involved, inspection of the relationship of C/Co us. In (-ln (C/ C,)) will show that errors in In k become largest a t both small and large values of C/CO. Thus, it is recommended that for accurate determinations, C/C, should preferably be near 0.5, and within limits of 0.2 to 0.8. This can readily be accomplished by means of the variable reaction conditions: the flow rate of carrier gas and the choice of thermolysis temperature.
Reactor Model The performance of the flow tube thermolysis apparatus has been carefully established to ensure that data are given correct interpretation. It will be shown that the reactor behaves very nearly as an ideal static reactor. This extremely simple result is developed from the axial dispersion model of mixing for a tubular reactor operated at the conditions of these experiments. The flow in the reactor is clearly laminar, far the maximum Reynolds number is 3.2. From the Graetz’ solution for heat transfer from the wall to the flowing fluid, the cold gas entering the reactor attains (within 0.1”) the wall temperature in less than 1 cm. I n addition, the parabolic velocity profile also is achieved in less than 0.1 cm of tube length. The preesure drop across the reactor is so small that the flow is incompressible. Thus the flow in the reactor is fully developed laminar (parabolic velocity profile), isothermal, and incompressible. Taylor* developed the axial dispersion model for laminar flow in long tubes. I n this model the fluid is considered to flow as a piston in a cylinder. Radial diffusion interacts with the parabolic velocity profile to provide an axial diffusive flux relative to the assumed piston flow. Strictly, the model only applies to systems which satisfy the inequality
(NR,/Ns,) < 30(l/d) (3) where N R e is the Reynolds number, Ns, is the Schmidt number (kinematic viscosity divided by diffusivity), d is the inside tube diameter, and 1 is the reactor length. This inequality is most certainly valid after 1-cm length in these experiments. I n addition, Farrell and Leonards developed an analysis for mixing in the entrance region of pipe in laminar flow; it was shown that the mixing is (6) F. 0.Rice, “Free Radicals” (Collected Papers), The Catholict University Press, Washington, D. C., 1958. (7) H. Grober, S. Erk, and U. Grigull, “Fundamentals of Heat Transfer,” McGraw-Hill Book Co., Inc., New York, N. Y.,1961. (8) G. I. Taylor, Proc. Roy. Soc., A219, 186 (1953); A225, 473 (1954). (9) M. J. Farrell and E. F. Leonard, A.I.Ch.E. J.,9, 160 (1962).
HOMOGENEOUS GAS-PHASE THERMOLYSIS KINETICS greater in the entrance region than in the zone for which the Taylor model applies. Thus the use of the Taylor model for mixing in the reactor appears to be well justified but slightly conservative. The thermolysis reaction is kinetically first order and thus the reactor performance is uniquely specified by the residence time distribution. I n dimensionless form the component material balance for the reactor is written as
4059 simple way of relating this transfer function to the measured parameters of the experiment is through moment analysis. The measured values are the area of the chromatographic peak for reactant prior to entering the reactor and the area of this peak after passing through the reactor, These areas are equivalent to the zeroth moments of P and C. The zeroth moments are found directly by taking the limit as s approaches zero. Denoting the moments as Moc, etc., the general equation is
Mo" = MoFMoT
Thus MOT,the zeroth moment of the reactor transfer function, is the fraction of the reactant remaining. I n terms of the parameters of the problem
where
Dax P = -, the axial dispersion parameter ul IC K = -, the kinetic reaction parameter
ReA+K
+ K ) sinh R + R cosh R where A = (2P)-' and R = d1 + 4PK/2P. The e-= e-K(
U
Z = x/Z, dimensionless length T = tv/l, dimensionless time C = C/Cref,dimensionless concentration
Thus the performance of the reactor is described by two parameters: K , the reaction rate parameter which is the object of this study, and P , the axial dispersion parameter which is estimated from the Taylor model. The boundary conditions for eq 4 have been discussed extensively,1° and for this study are chosen as
F(t) = C
- P -bC at2 bZ
=0
(6)
and
bC
-=
dZ
(8)
term of eq 9 is the performance of an ideal static reactor, and the term in parentheses is a correction factor for axial dispersion. Three limiting values of MOT are found easily and are listed as ideal static reactor: MOT= e-K as P -F 0 ideal stirred tank reactor: MOT=
1 as P
-F
co
+
zero reaction rate: MOT= 1 for K = 0 and any P The zero reaction rate limit is a statement of conservation of mass. When the axial dispersion parameter P is small the correction term in eq 9 can be expanded to yield
Oat2 = 1
(A
The initial condition for an empty reactor is C(2,O) = 0. Equation 5 is written in terms of an arbitrary forcing function, F(t). Physically F(t) is the pulse of reactant in carrier gas which is injected into the reactor. The solution to eq 4 is obtained by Laplace transformation with respect to T and solution of the ordinary differential equation subject to the boundary conditions, eq 5 and 6. Denoting transform variables by overbars, the result is
(A
+
ReA+K K ) sinh R R cosh R
+
(1
+ K2P + ($ - 2)K2P2 . . .)
(10)
The terms in eq 10 will converge rapidly where P is less than 0.01 for the values of K used in this experimental work. The analysis which follows demonstrates that the correction to the static model is small enough to be ignored. The apparent rate constant for a static reactor is defined as
K a p p= -In MOT where rl =
r2 =
1
2P 1
1+K2P+
+ d1 + 4P(s + K ) - dl + 4P(s + K ) 2P
and s = Laplace transform variable. The term in brackets is the transfer function for the reactor. A
=
K
- K2P
(4'- -
2)K2P2 . .
.)
+ 2K2P2 . . .
(11) Equation 11 is a quadratic expression for the true K in terms of the apparent K . Upon expanding the final form of eq 11 one finds (IO) F. J. Wehner and R. H. Wilhelm, Chem. Eng. Sei., 6,89 (1966); 8 , 309 (1958).
Volume 73, Number 1.2 December 1060
4060
H. KWART, S. F.SARNER,AND J. H.OLSON
Table I : Mixing Correction Factors
T , OK
MOT
793 793 823 823 844 866 872 883 893
0.706 0.661 0.665 0.483 0.455 0.242 0.363 0.263 0.206
Inverse Peelet no., D/vd
Kapp
0.348 0.414 0.405 0.727 0.787 1.419 1.013 1.336 1.578
P x
10'
Correction factor
Ktrue
1.000387 1.000477 1.000275 1.000597 1.000543 1.000979 1.000629 1.000829 1.000979
0.348 0.414 0 405 0.727 0.787 1.420 1.014 1.337 1.579
0.089 0.114 0.030 0.058 0.031 0.031 0.016 0.016 0.016
1.11 1.15 0.68 0.82 0.69 0.69 0.62 0.62 0.62
c/co
k, sec-1
In A
0.711 0.704 0.661 0.674 0.660 0.666 0.485 0.483 0.482 0.446 0.448 0.450 0.467 0,465 0.237 0.248 0.242 0.241 0.356 0.370 0.363 0.259 0,266 0.264 0.210 0.196 0.213
0,033 0.034 0.031 0.118 0.124 0.122 0.112 0.113 0.113 0.246 0.245 0.243 0,232 0.233 0.452 0.438 0.446 0.447 0.638 0.614 0.626 0.844 0.828 0.832 0.985 1.029 0.977
-3.40 -3.37 -3.47 -2.14 -2.09 -2.11 -2.19 -2.18 -2.18 -1.40 -1.41 -1.41 -1.46 -1.46 -0.79 -0.83 -0.81 -0.81 -0.45 -0.49 -0.47 -0.17 -0.19 -0.18 -0.015 -0.029 -0.023
I
Table I1 : Gas-Phase Thermolysis Kinetics of Ethyl Acetate
Temp, "C
10a/T, OK
Flow rate,a ml/min
Residence time, see
472.0
1.342
9.56
10.22
498 6
1.296
7.35 28.20
13.29 3.34
14.58
6.47
I
0
517.5
1.265
28.04
3.28
537.1
1.234
28.20
3.19
543.0
1.225
55.07
1.62
552.4
1.211
55.07
1.60
561.3
1.198
55.07
1.58
Flow rate corrected for measurement a t 25.0'.
K =~
+
-
.
~ K ~~ ~ ~~ 2 P~ ()( .) .~i
(129
The application of eq 12 for data reduction requires estimates of the axial dispersion parameter. Taylors developed a theoretical model for the effective diffusivity which was carefully tested in the experimental work of Bournia, Coull, and H0ughton.l' Figure 4 shows these results combined with additional experimentation. There is a shallow minimum in the group, PZ/d, for inverse Pecl6t numbers (DJud) in the range 0.01 to 0.1. There is no current theoretical model for this curve although the asymptotes have proper values. This empirical correlation was used to estimate P. The Journal of Physical Chemistry
Table I lists the data used in the examination. The correction factor is the term 1 KapPP(l- 2 P ) , the ratio by which the apparent rate constants must be multiplied to obtain the true value. The correction factor ordinarily is unity within experimental error limits. Thus, the thermolysis reactor effectively is a static reactor with a reaction time equal t,o the pulse residence time, and the dimensionless rate parameter, K , is found from the simple static reactor model as
+
K
=
k~
= -In
(C/C,)
(13)
(11) A. Bournia, J. Coull, and G . Houghton, Proc. Roy. Soc., A261, 227 (1961).
HOMOGENEOUS GAS-PHASE THERMOLYSIS KINETICS
4061
z c w
H OAc
Et Ac Figure 5.
F
c 2 H4
-
t):
/
e -
PISTON FLOW DIFFUSION
0ST DATA (LOUWI
ft;, -1z
MOLECULAR INVERSE P E C L ~ T NUMBER
8
4
Thermolysis of Ethyl Acetate as a Test Case The thermolysis of ethyl acetate was chosen as a test reaction due to its simplicity and the abundance of kinetic data available in the literature for compari~on.4,'~-'7 The mechanism has been established as a cis elimination (Figure 5 ) proceeding through a sixmembered ring cyclic transition state to the acid and olefin. Thus, the only species present should be ethyl acetate, acetic acid, and ethylene, in addition to any standards and/or solvents used. Examination of both flame ionization detector traces and the "small molecule" thermal conductivity chromatograms proved this to be the case. Data were obtained for a range of temperatures from 472 to 561" and at flow rates of about 7-55 ml/min. The results (Table 11) were fitted by regression analysis to the basic Arrhenius equation with the results = 1,87 X 1012e-46,700/RT see-1
* 0 . 7 kcal/mol = 28.26 * 0.46sec-' = 12.27 * 0 . 2 0 sec-'
E = 46.7 1nA log A
AS* = -6.3
f
1.0eu
As can be seen from Table I11 and Figure 6, this result -
~~
Temp range, "C
-2-
-li 1.15
A E = 46.7 i 0 7 kcallmole I ~ A =2 8 2 6 046seC' lagA :12 27 f 0 20 s e C '
*
AS*, -6.3 IOe u. LOWEST DATA
1.20
1.25
1.30
1.39
RECIPROCAL TEMPERhTURE. 1031T
Figure 6.
is in excellent agreement with previous values and lies about midway in the range of values previously obtained.
Thermolysis of endo-Dicyclopentadiene as a Test Case The thermolysis of endo-dicyclopentadiene is another excellent test case since reliable data exist in the literat ~ r e , ' ~ , 'and 9 since the reaction is also a simple one involving only the fission of dicyclopentadiene into two cyclopentadiene molecules. Since the presence of highly acidic products was not desired in one of the systems, this reaction was chosen as an additional test case and as a check on the comparability of data obtained from different reactors. I n the two smallest reactors (4.07 and 3.67 cma) data were obtained over the temperature ranges of 244-282 and 240-280' , while in the largest i:eactor the range of 200-250' was investigated (see Tables IV-VI). Since each set of data was taken over a comparatively
~
Table I11 : Comparison of Ethyl Acetate Thermolysis Data
386-487 500-603 514-610 433-461 437-465 472-561 452-537 434-531
k 3 1.87 x 10lZe-46700/R~se
W
Figure 4.
T A r r h e n i u s parameters--log A , 8 8 0 - 1 A E , kcal/mol
12.84 12.59 12.49 12.47 12.38 12.27 12.10 11 -97
48.3 48.0 47.7 47.7 47.4 46.7 46.5 46.3
Reference
17 13 14 16 16 This work 12 4
(12) J. C. Scheer, E. C. Kooyman, and F. L. J. Sixma, Rec. Trav. Chim., 82 ( l l ) , 1123 (1963); J. C. Scheer, Thesis, Amsterdam, Netherlands, 1961. (13) A. T. Blades and P. W. Gilderson, Can. J. Chem., 38, 1407 (1960). (14) A. T. Blades, ibid., 32, 366 (1954). (15) C. H. DePuy and R. W. King, Chem. Rev., 60,431 (1960). (16) C. A. Cramers, Thesis, Eindhoven, Netherlands, 1967; C. A. Cramers and A. I. M. Keulemans, J . Gas Chromatogr., 5 , 58 (1967). (17) R. Louw, Thesis, Leiden, Netherlands, 1964. (18) J. B. Harkness, G. B. Kistiakowsky, and W. H. Mears, J. Chem. Phys., 5, 682 (1937). (19) W. C. Herndon, C. R. Grayson, and J. M. Manion, J . Org. Chem., 32, 526 (1967). Volume 73, Number 1.9
December 1060
